The purpose of this lab is to determine the relationship between the angle of elevation and the energy lost to friction. This will be done by using a cart with a spring, a photogate, a nearly frictionless track, and a laptop. First the spring constant of the spring on the cart will be determined. Then we will measure the change in energy at various angles of elevation. We hypothesize that as the angle of the elevation of the track increases, the energy lost due to friction will increase proportionately.
Procedure
Part I: The Determination of the Spring Constant.
The experiment was set up using a track and photogate on a flat surface. The cart was propelled forward by its spring through the photogate, which recorded the gate time at approximately the initial velocity. Using the gate time and the width of the photomarker, we calculated the velocity of the cart in m/s. Using that velocity and the previously weighed mass of the cart we calculated the kinetic energy. We set this kinetic energy equal to the spring energy of the cart. Using the length of the spring we were able to determine the spring constant.
Part II: The Effect of Elevation on Energy Loss due to Friction
In the second part of the experiment, we treated the angle of elevation of the track as the variable. Starting with a small angle of elevation we released the spring on the cart to send it up the track and recorded the distance it traveled up the track. We did multiple trials at each elevation and recorded the approximate location where the carts stopped moving. This gave us the final potential energy of the cart because we found the vertical height. Then we used trigonometry to find the angle of incline for each different elevation.
Results
Calculation of Spring Constant
Velocity(m/s)
KE(J)
SE(J)
K(N*m)
Ave. K (N*m)
.96266
.246
.246
200.8
.92857
.229
.229
186.9
.89655
.213
.213
173.9
.89655
.213
.213
173.9
.92857
.229
.299
186.9
184.5
Theoretical Energy Value from Spring: .226J
We used this value to calculate the energy lost at the two different elevations.
These tables describe the height of the car from the ground when at rest of the track,from there we were able to calculate the potential energy and the energy lost by taking the difference from the theoretical energy value.
Angle of Elevation:6.1595 degrees
Height(cm)
PE(J)
Energy lost(J)
Ave. Energy lost(J)
8.69
.222
.004
8.89
.227
-.001
8.39
.214
.012
8.19
.209
.017
8.59
.219
.007
8.19
.209
.017
7.89
.197
.029
.012
Angle of Elevation:6.8316 degrees
Height(cm)
PE(J)
Energy lost(J)
Ave. Energy lost(J)
7.98
.204
.022
7.45
.190
.036
8.08
.207
.019
7.98
.204
.022
8.08
.207
.019
7.98
.196
.030
8.08
.207
.019
.023
Conclusions
As the angle of elevation increased from trial 1 to trial 2, the energy lost to friction also increased substantially. We conclude that this is because the downward force of gravity is pushing the cart against the track, and the downward force of gravity is in sharper contrast with the greater incline. The cart loses more energy to friction when it goes up a steeper slope and this makes sense because if the ramp was angled close to 90 degrees, their would be almost no movement.
The trials for the first two angles of elevation agreed with our hypothesis. However, when trying the experiment on a third angle of elevation, 9.06 degrees, our results for some reason indicated that the cart at the end has greater energy than the cart at the beginning, meaning that there is some error in our trials for the third angle of elevation, perhaps a possible rounding or measurement error.
Table of Contents
Title
Nikhil, Tarun, Annelise, Dominic
Introduction
The purpose of this lab is to determine the relationship between the angle of elevation and the energy lost to friction. This will be done by using a cart with a spring, a photogate, a nearly frictionless track, and a laptop. First the spring constant of the spring on the cart will be determined. Then we will measure the change in energy at various angles of elevation. We hypothesize that as the angle of the elevation of the track increases, the energy lost due to friction will increase proportionately.
Procedure
Part I: The Determination of the Spring Constant.
The experiment was set up using a track and photogate on a flat surface. The cart was propelled forward by its spring through the photogate, which recorded the gate time at approximately the initial velocity. Using the gate time and the width of the photomarker, we calculated the velocity of the cart in m/s. Using that velocity and the previously weighed mass of the cart we calculated the kinetic energy. We set this kinetic energy equal to the spring energy of the cart. Using the length of the spring we were able to determine the spring constant.
Part II: The Effect of Elevation on Energy Loss due to Friction
In the second part of the experiment, we treated the angle of elevation of the track as the variable. Starting with a small angle of elevation we released the spring on the cart to send it up the track and recorded the distance it traveled up the track. We did multiple trials at each elevation and recorded the approximate location where the carts stopped moving. This gave us the final potential energy of the cart because we found the vertical height. Then we used trigonometry to find the angle of incline for each different elevation.
Results
Calculation of Spring ConstantTheoretical Energy Value from Spring: .226J
We used this value to calculate the energy lost at the two different elevations.
These tables describe the height of the car from the ground when at rest of the track,from there we were able to calculate the potential energy and the energy lost by taking the difference from the theoretical energy value.
Angle of Elevation:6.1595 degrees
Angle of Elevation:6.8316 degrees
Conclusions
As the angle of elevation increased from trial 1 to trial 2, the energy lost to friction also increased substantially. We conclude that this is because the downward force of gravity is pushing the cart against the track, and the downward force of gravity is in sharper contrast with the greater incline. The cart loses more energy to friction when it goes up a steeper slope and this makes sense because if the ramp was angled close to 90 degrees, their would be almost no movement.
The trials for the first two angles of elevation agreed with our hypothesis. However, when trying the experiment on a third angle of elevation, 9.06 degrees, our results for some reason indicated that the cart at the end has greater energy than the cart at the beginning, meaning that there is some error in our trials for the third angle of elevation, perhaps a possible rounding or measurement error.